Probability and Statistics Index > Critical Values > Z Score to Percentile

## How do I Convert a Z Score to Percentile?

Use a calculator, like the one below, or use a table (see instructions further down) and calculate the percentile by hand. In either case, you will be more easily able to convert a z score to a percentiles if you know some basics about normal distributions, like the 68 95 99.7 rule. This rule states that 68 percent of the area under a bell curve lies between -1 and 1 standard deviations either side of the mean, 94 percent lies within -2 and 2 standard deviations and 99.7 percent lies within -3 and 3 standard deviations; these standard deviations are the “z scores.” If you need some basic info on bell curves, see:

What is a Bell Curve?

### Basic Z Table

A Z Table has z scores and their associated areas. Once you have found the area, convert that to a percentile. This mini table shows the area for z scores in .5 increments:

For example, let’s say you wanted to convert a z score of -2 to a percentile. The area listed in the table is .0227. To convert this decimal to a percentile, move the decimal point two places to the right and then add a percentage sign:

.0227 becomes 2.27%

Things become a little more tricky when you want a z score that’s not listed in the table above. In that case, you should use a more comprehensive z-table.

## Z Score to Percentile Example

- Look up the value in the z-score in the z-table:

Check out our YouTube Channel for hundreds of elementary statistics videos!

------------------------------------------------------------------------------**Need help with a homework or test question?**With Chegg Study, you can get step-by-step solutions to your questions from an expert in the field. Your first 30 minutes with a Chegg tutor is free!*Statistical concepts explained visually*- Includes many concepts such as sample size, hypothesis tests, or logistic regression, explained by Stephanie Glen, founder of StatisticsHowTo.**Comments? Need to post a correction?**Please post a comment on our*Facebook page*.